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Excel in math and science
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Higher-order Derivatives
The first derivative is the slope of a curve, and the second derivative is the slope of the slope, like acceleration. So what's the third derivative? (Fun fact: it's actually called jerk.)
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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Concept Quizzes
Let \(f\) be a function such that \(f(0)=50.\) If the above graph represents the graph of the first derivative of \(f\) on the interval \(0<x<3,\) which of the following is the correct description of \(f\) on this interval?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
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For the function \(y=x^3+x^2-x-1,\) determine the interval where \(y\) is decreasing.
Excel in math and science
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Suppose \(f\) is a function such that \(f(0)=33\) and the first derivative of \(f\) on the interval \(-2 < x < 2\) is as shown in the above diagram. Which of the following is the correct description of the function \(f\) on this interval?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
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Used and loved by 4 million people
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Suppose \(f\) is a function defined on the closed interval \(-3 \le x \le 4\) with \(f(0)=42,\) such that the graph of \(f',\) the derivative of \(f,\) on the interval is as shown in the above diagram. On what intervals is \(f\) increasing?
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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including olympiad champions, researchers, and professionals.
Suppose \(f\) is a function defined on the closed interval \(-3 \le x \le 4\) with \(f(0)=3\) such that the graph of \(f',\) the derivative of \(f,\) on the interval is as shown in the above diagram. Find the \(x\)-coordinates of the points of inflection of \(f.\)